3 citations · 3 across the 6 of their papers we have counts for
4 papers · 1 filter
Variationally correct loss functions for nonlinear parametric problems and their neural approximations
Pablo Cortés Castillo, Wolfgang Dahmen, Jay Gopalakrishnan
We construct computable a posteriori error estimators for parametric families of nonlinear elliptic problems by measuring the residual of a variational formulation in the dual norm…
Global error estimators for parametric monotone nonlinearities and neural approximations
Pablo Cortés Castillo, Wolfgang Dahmen, Jay Gopalakrishnan
We construct computable error estimators, which double as loss functions for neural networks, for a class of parametric nonlinear partial differential equations with a monotonicity…
Sampling and reconstruction of convex functions
Andrea Bonito, Albert Cohen, Wolfgang Dahmen +3
We discuss optimal recovery for classes of multivariate convex functions from given point samples, as well as the sampling numbers of these classes, corresponding to optimal sample…
Preconditioning and Numerical Stability in Neural Network Training for Parametric PDEs
Markus Bachmayr, Wolfgang Dahmen, Chenguang Duan +1
In the context of training neural network-based approximations of solutions of parameter-dependent PDEs, we investigate the effect of preconditioning via well-conditioned frame rep…